Contributors A. S. ARGON ROGER F. BARTHOLOMEW F. M. ERNSBERGER S. W. FREIMAN ROBERT GARDON HARMON M. GARFINKEL GLASS: SCIENCE AND TECHNOLOGY Edited by D. R. UHLMANN DEPARTMENT OF MATERIALS SCIENCE AND ENGINEERING MASSACHUSETTS INSTITUTE OF TECHNOLOGY CAMBRIDGE, MASSACHUSETTS N. J. KREIDL DEPARTMENT OF CHEMICAL AND NUCLEAR ENGINEERING UNIVERSITY OF NEW MEXICO ALBUQUERQUE, NEW MEXICO VOLUME 5 Elasticity and Strength in Glasses (yjP) 1980 ACADEMIC PRESS A Subsidiary of Harcourt Brace Jovanovich, Publishers New York London Toronto Sydney San Francisco COPYRIGHT © 1980, BY ACADEMIC PRESS, INC. ALL RIGHTS RESERVED. NO PART OF THIS PUBLICATION MAY BE REPRODUCED OR TRANSMITTED IN ANY FORM OR BY ANY MEANS, ELECTRONIC OR MECHANICAL, INCLUDING PHOTOCOPY, RECORDING, OR ANY INFORMATION STORAGE AND RETRIEVAL SYSTEM, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHER. ACADEMIC PRESS, INC. Ill Fifth Avenue, New York, New York 10003 United Kingdom Edition published by ACADEMIC PRESS, INC. (LONDON) LTD. 24/28 Oval Road, London NW1 7DX Library of Congress Cataloging in Publication Data Main entry under title: Elasticity and strength in glasses. (Glass ; v. 5) Includes index. 1. Glass. 2. Elasticity. I. Uhlmann, Donald Robert. II. Kreidl, N. J. III. Series. TP848.G56 vol.5 [TA450] 666Ms [620.Γ4432] 80-38 ISBN 0-12-706705-1 (v. 5) PRINTED IN THE UNITED STATES OF AMERICA 80 81 82 83 9 8 7 6 5 4 3 2 1 List of Contributors Numbers in parentheses indicate the pages on which the authors' contributions begin. A. S. ARGON (79), Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ROGER F. BARTHOLOMEW (217), Corning Glass Works, Sullivan Park, Corning, New York 14830 F. M. ERNSBERGER(l,133),PPG/rcrfwsines, Inc., Pittsburgh, Pennsylvania 15238 S. W. FREIMAN (21), Fracture and Deformation Division, National Bureau of Standards, Washington, D.C. 20234 ROBERT GARDON (145), Engineering and Research Staff, Ford Motor Company, Dearborn, Michigan 48121 HARMON M. GARFINKEL (217), Corning Glass Works, Sullivan Park, Corning, New York 14830 Vll Preface Recent years have seen a notable series of developments that have emphasized the importance of amorphous solids (glasses). These include activity in the areas of fiber optics, optical waveguides, amorphous semi­ conductors, glass lasers, glass-ceramic materials, and photochromic glasses, to name only a few. In addition to advances related to these areas of technological application, there have also been notable improvements in our understanding of the structure, processing, and properties of glass- forming materials. Regrettably, most of the information developed in these areas is contained in a myriad of individual research papers and in-house knowledge, rather than in any convenient central reference source. The time seemed appropriate, therefore, to bring together the available knowl­ edge about this important class of materials. "Glass: Science and Technology," of which this volume is the first to appear, will be broad in its scope. The topics covered will range from fun­ damental understanding of the structure and properties of glasses—based on applying the disciplines of physics, chemistry, and materials science to amorphous materials—to highly applied areas such as the melting of glass, its forming in various shapes, and the use of glass in various important technological applications. Wherever possible, the common features and notable differences between glasses and other types of materials will be highlighted. At this time 12 volumes are planned. The tentative program is 1 Structure of Glass 2 Submicrostructure of Glass 3 Glass Forming Systems and Glass Ceramic Materials 4 Diffusion, Viscous Flow, and Relaxation Phenomena 5 Elasticity and Strength in Glasses 6 Electrical Properties of Glasses 7 Optical Properties of Glasses 8 Processing of Oxide Glasses 9 Processing of Polymers 10 Thermal and Magnetic Properties of Glasses 11 Glass Surfaces 12 Tabulation of Data IX X PREFACE In view of the rapid progress in understanding and controlling mechani­ cal properties during the past years it seemed appropriate to come out with Volume 5 first. It appears that much of the confusion about competitive views of glass as brittle or deformable can now be resolved by relatively simple concepts. Engineers have developed and successfully used ideas that clearly distin­ guish the mechanical properties of the glass from the influence of the num­ ber, distribution, size, and shape of flaws, particularly in the surface. Frac­ ture mechanics has been mobilized to predict strength and lifetime under defined service conditons. The classic art of increasing surface strength by compression in the flawed surface layer, using controlled quenching, has been subjected to careful analysis leading to improved products. At the same time numerous new methods of introducing compression layers by manipulating composition and structure have become available and are understood in considerable detail. The editors are confident that in this treatise the dissemination of the most recent knowledge and its use in this field has been entrusted to highly competent workers. GLASS: SCIENCE AND TECHNOLOGY, VOL. 5 CHAPTER 1 Elastic Properties of Glasses F. M. Ernsberger PPG INDUSTRIES, INC. PITTSBURGH, PENNSYLVANIA I. Introduction 1 II. The Nature of Elasticity in Glasses 2 III. Measurement of Elastic Constants 3 IV. Prediction of Elastic Constants 4 V. Empirical Correlations 5 VI. The Acoustoelastic Effect 7 VII. Phase Separation 8 VIII. Anomalous Elastic Properties of Glasses 9 A. Compressibility 9 B. Non-Hookean Behavior 10 C. Strain Dependence of Poisson's Ratio 11 D. Temperature Dependence of Elasticity 11 IX. Hardness 12 X. Microplasticity 14 References 17 I. Introduction This review is limited to vitreous silica and the silicate glasses, including those that contain moderate amounts of other network formers such as B 0 , A1 0 , and P 0 . Chalcogenide, metallic, and organic glasses are spe­ 2 3 2 3 2 5 cifically excluded, although certain concepts may be applicable to these glasses as well. It is assumed that the reader is familiar with the definitions and interre­ lationships of the three constants used in small-deformation stress-strain analysis of isotropic materials. With minor exceptions, glasses are fully isotropic, even in the form of drawn fibers. No attempt has been made to assemble data as such; the treatment is meant instead to identify concepts that have general validity and to empha­ size recent developments. The older literature, including much systematic Copyright © 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-706705-1 2 F. M. ERNSBERGER property data, is reviewed in a treatise by Morey (1954). The subject is also briefly reviewed in a recent treatise by Babcock (1977). In the final two sections, the discussion will depart from the domain of true elasticity to provide an introduction to the interesting and controversial behavior of glass at very high levels of stress, such as those applied in an indentation hardness test. Under these conditions, brittle glasses behave in what looks very much like a plastic manner. II. The Nature of Elasticity in Glasses There is a widespread opinion that glasses are supercooled liquids and therefore have a finite viscosity at ordinary ambient temperatures. Stories are told of glasses flowing under their own weight: of ancient windowpanes that are thicker at the bottom; of glass that has sagged in storage. These observations must find other explanations, because glasses of commercially useful compositions are in fact rigid solids at ordinary temperatures. Vit­ reous silica in particular is a nearly ideal elastic material; that is, it does not creep under load, and it recovers instantly after a prolonged deformation. On the other hand, glasses that contain substantial amounts of network- modifying oxides (NagO, CaO, etc.) often exhibit both creep and delayed recovery. It is probably this behavior that is responsible for many of the observations that have been erroneously ascribed to cold viscous flow. These delayed-elastic effects have such long relaxation times that they are sometimes difficult to distinguish from true viscous flow. Douglas (1966) stated that "any experiment which purports to measure a viscosity greater than 1016 poises needs to be examined extremely carefully." The atomic mechanisms responsible for these ambient-temperature vis- coelastic effects have not been fully explicated, but there is little doubt that monovalent cations are involved. The mobility of these ions is severely restricted by steric and electrostatic considerations, but nevertheless inter­ nal-friction and conductivity measurements show that cation mobility is detectable down to temperatures approaching that of liquid nitrogen. The time-dependent nature of the stress-strain behavior of glasses natu­ rally becomes more pronounced as the temperature is raised. These effects constitute a specialized technical study that will be discussed under the general topic "Relaxation Phenomena" in this volume. For present pur­ poses it is enough to state that the time dependence of mechanical behavior of the glasses under consideration is seldom large enough to influence the measurement of elastic constants, particularly at the high measurement fre­ quencies normally employed. A more-significant consideration, and one peculiar to glasses, is the state of anneal, sometimes termed "stabilization." The elastic constants, along 1. ELASTIC PROPERTIES OF GLASSES 3 with density, refractive index, and other intensive properties, change sig­ nificantly with the rate of cooling of a glass through its "transformation range." The transformation range of a glass may be defined as that temper­ ature range within which its properties spontaneously change at an experi­ mentally observable rate. The property changes arise from changes in the density of packing. Obviously the limits of this range have no fundamental definition, but are determined by the time allotted to the experiment and by the sensitivity of the measurement. In practical terms, the existence of this stabilization effect means that property data of extraordinary precision have no particular absolute significance unless the thermal history of the sample is carefully specified. III. Measurement of Elastic Constants Ultrasonic techniques continue to be favored for measurement of the elastic constants of glasses. Manghnani and his co-workers specialize in this field. They have elevated the pulse-echo technique to new levels of precision and accuracy by the superposition of pulses and echoes in the manner of interferometry. Even the elusive Poisson ratio is being reported to four significant figures. With such precision at hand, it becomes profitable to study the effects of pressure and temperature on the elastic constants. Manghnani et al. (1969) measured the constants for Vycor high-silica glass to 8 kbar. Skolowski and Manghnani (1969) measured calcium aluminate glasses to 3.5 kbar. Subse­ quently, Manghnani (1972) measured six glasses in the Na20-Ti0 -Si0 2 2 system to 7 kbar and 300°. Manghnani (1974) has also studied the new low- expansion glasses in the Si0 -Ti0 system as a function of temperature, 2 2 pressure, and composition. Data on a commercially produced soda-lime glass to 400° are awaiting publication. An elegant new measurement technique appeared recently with the pub­ lication of a paper by Huang et al. (1973) on a determination of elastic constants by Brillouin scattering. A few words about the principles under­ lying this unusual technique are appropriate. At any temperature above absolute zero, all elastic solids contain ther­ mally activated density fluctuations that propagate within the solid in all directions at sonic velocities with many superimposed frequencies. If a transparent elastic solid is probed with a laser, Brillouin scattering occurs from those trains of density waves whose frequency and direction of prop­ agation happen to satisfy the Bragg condition for the laser beam; Rayleigh scattering occurs as well, of course. Thus the spectrum of the scattered light consists of five lines: a central Rayleigh peak at the laser frequency flanked symmetrically by pairs of sum-and-difference peaks. One pair 4 F. M. ERNSBERGER reveals the frequency of the longitudinal acoustic mode; the other, that of the transverse mode. Thus it is possible to calculate both Young's modulus and the shear modulus and, from these, Poisson's ratio. The acoustic frequencies involved are in the hypersonic range; that is, in gigahertz. Nevertheless the elastic constants are not distinguishably differ­ ent from those measured at low frequencies. An unusual ultrasonic technique was described by Fräser and LeCraw (1964). The elastic constants were deduced from observations of reso­ nances excited in a small spherical specimen. Soga and others (1967, 1968) subsequently applied this technique in several interesting studies of glasses and ceramics. The main advantage seems to be in the small size (300 /xm- 5 mm) and simple geometry of the samples that are used. A novel method for the measurement of elastic constants was demon­ strated by Sinha (1977). A strip of elastic material whose thickness is not too small relative to its width will exhibit a saddle-shaped (anticlastic) cur­ vature when bent. The elastic constants can be deduced from appropriate measurements of this complex curvature. The results are not highly precise (only two significant figures were obtained), but the method has the advan­ tage that it is applicable at elevated sample temperatures when noncontact- ing optical methods are used to obtain the curvatures. Elastic constants can sometimes be estimated from information that might seem to be totally unrelated. For example, Szigeti (1950) proposed an equation relating the bulk modulus of crystals to the maximum fre­ quency of infrared reflection. Anderson (1965) subsequently demonstrated the applicability of this equation to glass. The existence of this relationship illustrates the great fundamental signif­ icance of elastic constants, related as they are to interatomic forces and vibrational frequencies. Sanditov and Bartenev (1973) have proposed rela­ tionships between bulk modulus and still other solid-state properties such as thermal expansion coefficient, glass transition temperature, and micro- hardness. It does not appear that these have yet been independently verified. IV. Prediction of Elastic Constants One of the ultimate goals of scientific endeavor is to make empirical mea­ surements unnecessary. This goal has been attained when our understand­ ing of a phenomenon becomes so profound that the desired quantities can be calculated from a few fundamental constants. A paper by Makishima and Mackenzie (1973) embodies a significant degree of progress in this direction. The derivation is adapted from an existing theoretical treatment of